Artificial Tsunami

ABSTRACT

An artificial tsunami is a new type of beaching tactic capable of achieving the military goal with almost no losses among the invading forces.

BRIEF SUMMARY

An artificial tsunami is a new type of beaching tactic capable of achieving the military goal with almost no losses among the invading forces.

BACKGROUND

In World War II, the Normandy Invasion was the key to the victory of the Allied Forces. However, the number of soldiers required for beaching was up to five to ten times the number of enemy, which resulted in heavy losses. Thus, when a beaching tactic is demanded, using an artificial tsunami to conduct operations first before dispatching forces to take over the situation would significantly reduce casualties.

DETAILED DESCRIPTION

At the proper distance from the beaching destination, an artificial tsunami can be created by having bombers above the designated coordinate points, as positioned by artificial satellite, to airdrop bombs equivalent to the designed value on the sea, controlling their underwater penetration with a pressure gauge and timer, and then exploding the bombs at the projected depth. 

1. The said artificial tsunami complies with the law of conservation of energy in Physics and its expression is ΔU+ΔK=0 After the undersea explosion, the bombers integrate the explosive kinetic energy and the drainage potential energy. They explode into a sphere in waveform and scatter in all directions; therefore, the energy for the drainage upward is just half of the explosive kinetic energy, and the theoretical formula can be expressed as: ${{\sum\limits_{i = 1}^{n}{m_{i}{g(\psi)}h_{i}}} - {\frac{1}{2}{K({TNT})}}} = 0$ Because sea water is an incompressible fluid, its explosive kinetic energy can be directly transformed into drainage potential energy. However, the consumption system of explosive energy φ(d) must be considered as well; therefore, the proper reduction coefficient of the explosive kinetic energy, as well as the situation of there being more depth of water d and more reduction of energy must be taken into consideration. On calculating its actual effect on the explosive energy of sea water, the conservation mode of the modified energy can be obtained as: ${{\phi (d)}{K({TNT})}} = {2{g(\psi)}{\sum\limits_{i = 1}^{n}{m_{i}h_{i}}}}$ The explosion of the bombs under the sea leads to a rise in sea level. The lateral plane of the rise is close to the scattering of the Gaussian distribution; so, it is assumed that the rise complies with the bell curve of the Gaussian distribution in Statistics. According to the measured data of the bomb explosion, or the data analyzed from computational fluid dynamics (CFD), the standard deviation in the density function of definitive probability, as well as the actual state of explosion, is derived. At the same time, consideration should also be given to the situation that the standard deviation increases along with the depth of the sea, i.e. ω(d) is the explosive waveform factor of a bomb. When selecting modified probability density function ƒ(x), and taking expected value μ=0 as the zero point of the bomb, as well as the measured or simulated standard deviation ω(d) and its amplified coefficient X, substituting the modified energy conservation formula will obtain the derivative formula: $\mspace{79mu} {y = {{f(x)} = {{{\frac{1}{{\omega (d)}\sqrt{2\pi}}^{- \frac{x^{2}}{2{({\omega {(d)}})}^{2}}}}\mspace{79mu}->x^{2}} = {{- 2}\left( {\omega (d)} \right)^{2}{\ln \left( {{\omega (d)}\sqrt{2\pi}y} \right)}}}}}$ $\mspace{79mu} {X = {\frac{h_{T}}{f(0)} = {\frac{h_{T}}{\frac{1}{{\omega (d)}\sqrt{2\pi}}} = {h_{T}{\omega (d)}\sqrt{2\pi}}}}}$ $\begin{matrix} {{{\phi (d)}{K({TNT})}} = {2\rho \; {g(\psi)}{\int_{0}^{\frac{1}{{\omega {(d)}}\sqrt{2\pi}}}{\left\lbrack {\left( {\pi \; x^{2}} \right){yX}^{3}} \right\rbrack {y}}}}} \\ {= {2\rho \; {g(\psi)}{\int_{0}^{\frac{1}{{\omega {(d)}}\sqrt{2\pi}}}{\begin{Bmatrix} {\pi \left\lbrack {{- 2}\left( {\omega (d)} \right)^{2}{\ln \left( {{\omega (d)}\sqrt{2\pi}y} \right)}} \right\rbrack} \\ {y\left( {h_{T}{\omega (d)}\sqrt{2\pi}} \right)}^{3} \end{Bmatrix}{y}{y}}}}} \\ {= {\sqrt{2}\pi^{\frac{3}{2}}\rho \; {g(\psi)}\left( {h_{T}{\omega (d)}} \right)^{3}}} \end{matrix}$ The above formula is expressed as K(TNT) to obtain the theoretical standard expression, which is: ${K({TNT})} = \frac{\sqrt{2}\pi^{\frac{3}{2}}\rho \; {g(\psi)}\left( {h_{T}{\omega (d)}} \right)^{3}}{\phi (d)}$ On the premise of ignoring the deviation of sea water density ρ and acceleration of gravity g(ψ), the constants of ρ and g(ψ) are substituted into the above formula to deduce the result, which is taken as the definition of the artificial tsunami created by a bomb. The artificial tsunami design formula is: ${K({TNT})} = \frac{79156\left( {h_{T}{\omega (d)}} \right)^{3}}{\phi (d)}$ By redefining the above constant with C_(T)=79156, the following artificial tsunami design formula is obtained: ${K({TNT})} = \frac{{C_{T}\left( {h_{T}{\omega (d)}} \right)}^{3}}{\phi (d)}$ Because a different explosion waveform ω(d) leads to a different sea water transmission attenuation rate β_(T)(ω(d),D), which is the function of explosion waveform ω(d), the distance between the coordinate points of the air-dropped bomb and the beaching destination is D; this is also a factor that influences sea water transmission attenuation rate β_(T)(ω(d),D). So, the design height of the beaching destination is h_(g), which is related to the maximum rise of tsunami design h_(T), and takes into consideration factor of safety (F.S.)_(T). The standard expression is: $h_{T} = \frac{\left( {F.S.} \right)_{T}h_{g}}{\beta_{T}\left( {{\omega (d)},D} \right)}$ After the bomb explodes under the sea, sea water capacity V led by the rising sea level is: $\begin{matrix} {V = {\int_{0}^{\frac{1}{{\omega {(d)}}\sqrt{2\pi}}}{\left\lbrack {\left( {\pi \; x^{2}} \right)X^{3}} \right\rbrack {y}}}} \\ {= {\int_{0}^{\frac{1}{{\omega {(d)}}\sqrt{2\pi}}}{\left\{ {{\pi \left\lbrack {{- 2}\left( {\omega (d)} \right)^{2}{\ln \left( {{\omega (d)}\sqrt{2\pi}y} \right)}} \right\rbrack}\left( {h_{T}{\omega (d)}\sqrt{2\pi}} \right)^{3}} \right\} {y}}}} \\ {= {4\pi^{2}{h_{T}^{3}\left( {\omega (d)} \right)}^{4}}} \end{matrix}$ In considering the actual effect of the sea water capacity of the artificial tsunami on the beaching destination, and in order to display the sea water capacity of the radial pattern of a fan-shaped region, the coordinate points of an air-dropped bomb on the sea and the maximum breadth of the beaching destination form an angle α; in considering the effect of sea water transmission attenuation rate β_(T)(ω(d),D) on the sea water capacity, the standard expression of the actual sea water capacity for beach destination V_(e) can be expressed as: $\begin{matrix} {V_{e} = {4\pi^{2}{{h_{T}^{3}\left( {\omega (d)} \right)}^{4} \cdot \frac{\alpha}{2\pi} \cdot \left( {\beta_{T}\left( {{\omega (d)},D} \right)} \right)^{3}}}} \\ {= {2{{\pi\alpha}\left( {h_{T}{\beta_{T}\left( {{\omega (d)},D} \right)}} \right)}^{3}\left( {\omega (d)} \right)^{4}}} \end{matrix}$ In considering the factor of safety and sea water capacity V_(r) meeting the demand of overflowing the beaching destination, the standard expression is: V _(e)=2πα(h _(T)β_(T)(ω(d),D))³(ω(d))⁴ ≧V _(r)((F.S.)_(T))³ When considering airdropping a bomb group, as individual bombs explode under the sea they influence each other, which may lead to the sea water capacity of the artificial tsunami failing to meet the original value. Therefore, it is reasonable to airdrop two lines of bombs with an equal explosion equivalent TNT at sea level. The following symbols “” are the airdropping points for the bombs. The order and the timing for airdropping must be arranged perfectly so as to achieve the maximum effect of the artificial tsunami.

Considering the mutual influence of the bomb group, which may lead to the “bomb group effect” and result in the artificial tsunami failing to meet the original value, it is necessary to modify the actual artificial tsunami sea water capacity V_(e). Under the bomb group effect of an artificial tsunami, the modified coefficient φ_(e)(S,R_(b)) of the explosive kinetic energy reduction coefficient φ(d) is related to the distance S and its effective explosion radius R_(b). The explosion of each bomb in the central area is influenced by the explosions of the two adjacent bombs, while the explosion of the two side bombs (on the two ends) is only influenced by the explosion of one, respective, adjacent bomb. Consequently, the modified coefficient of explosive kinetic energy φ_(e)(S,R_(b)) for the central area and for the two sides should be calculated according to the relationship with the neighboring bombs, respectively, and can be expressed as: ${\phi_{e}\left( {S,R_{b}} \right)} = \frac{V_{b,e}\left( {S,R_{b}} \right)}{V_{b,0}\left( R_{b} \right)}$ According to the explosive kinetic energy from the modified coefficient φ_(e)(S,R_(b)), the derived artificial tsunami waveform ω(d) will also be influenced. Consequently, under the bomb group effect of the artificial tsunami, the modified coefficient φ_(v)(S,R_(ω)) of sea water capacity V_(e) is related to the bomb group distance S and the effective explosion radius R_(ω). The modified coefficient of sea water capacity φ_(v)(S,R_(ω)) in the central area and on the two sides uses the same conditions as the modified coefficient of explosive kinetic energy φ_(e)(S,R_(b)), and should be calculated according to the relationship of the neighboring bombs: it can be expressed as: ${\phi_{v}\left( {S,R_{\omega}} \right)} = \frac{V_{\omega,e}\left( {S,R_{\omega}} \right)}{V_{\omega,0}\left( R_{\omega} \right)}$ In considering the bomb group effect, the theoretical standard expression of the single bomb explosion energy K_(e)(TNT) modified by the modified coefficient of explosive kinetic energy φ_(e)(S,R_(b)), is expressed as: ${K_{e}({TNT})} = \frac{\sqrt{2}\pi^{\frac{3}{2}}\rho \; {g(\psi)}\left( {h_{T}{\omega (d)}} \right)^{3}}{{\phi (d)}{\phi_{e}\left( {S,R_{b}} \right)}}$ where K_(e)(TNT)) is the single bomb explosion energy, and (K_(e)(TNT))_(n) is that of the aggregated bombs; its theoretical standard expression is: $\left( {K_{e}({TNT})} \right)_{n} = {\sum\limits_{i = 1}^{n}\frac{\sqrt{2}\pi^{\frac{3}{2}}\rho \; {g(\psi)}\left( {\left( h_{T} \right)_{i}{\omega \left( d_{i} \right)}} \right)^{3}}{{\phi_{i}\left( d_{i} \right)}\left( {\phi_{e}\left( {S_{i},\left( R_{b} \right)_{i}} \right)} \right)_{i}}}$ Sea water density ρ and acceleration of gravity g(ψ) of the above expression are substituted with their constants and redefined with C_(T)=79156, and the bomb group artificial tsunami design expression becomes: $\left( {K_{e}({TNT})} \right)_{n} = {\sum\limits_{i = 1}^{n}\frac{{C_{T}\left( {\left( h_{T} \right)_{i}{\omega \left( d_{i} \right)}} \right)}^{3}}{{\phi_{i}\left( d_{i} \right)}\left( {\phi_{e}\left( {S_{i},\left( R_{b} \right)_{i}} \right)} \right)_{i}}}$ In consideration of the bomb group effect, the standard expression of single bomb sea water capacity V_(e,e), after being modified by the modified coefficient of sea water capacity φ_(v)(S,R_(ω)), factor of safety and sea water capacity V_(r), as well as meeting the demand of overflowing the beaching destination, is: V _(e,e)=2παφ_(v)(S,R _(ω))(h _(T)β_(T)(ω(d),D))³(ω(d))⁴ >V _(r)((F.S.)_(T))³ With single bomb sea water capacity V_(e,e) according to the above expression, having considered sea water capacity (V_(e,e))_(n) of the aggregated bombs, factor of safety and sea water capacity V_(r) meeting the demand of overflowing the beaching destination, its standard expression is: $\begin{matrix} {\left( V_{e,e} \right)_{n} = {\sum\limits_{i = 1}^{n}{2{\pi\alpha}_{i}{\phi_{v}\left( {S_{i},\left( R_{\omega} \right)_{i}} \right)}\left( {\left( h_{T} \right)_{i}\left( {\beta_{T}\left( {{\omega \left( d_{i} \right)},D_{i}} \right)} \right)_{i}} \right)^{3}\left( {\omega \left( d_{i} \right)} \right)^{4}}}} \\ {\geq {V_{r}\left( \left( {F.S.} \right)_{T} \right)}^{3}} \end{matrix}$ Reduction coefficient φ(d) of the explosive kinetic energy and explosion waveform coefficient ω(d) are functions of the depth of the bombs in the water, but as the waveform of the functions is not necessarily linear, it is advisable to get the corresponding curve through actual measurement or to express its correspondence through multi-expressions. As for the underwater penetration d of the same bomb, the continuous increase in the explosion equivalent TNT of the bombs gradually reduces the value of explosion waveform coefficient (d), i.e. the explosion waveform gets steeper and steeper. As for the explosion equivalent TNT of the same bomb, the continuous increase in underwater penetration d gradually increases the value of explosion waveform coefficient (d), i.e. the explosion waveform becomes smoother and smoother. However, in consideration of the fact that the artificial tsunami must be able to reach the beaching destination, the artificial tsunami should be created with a higher explosion waveform coefficient ω(d). The artificial tsunami design formula should consider existing tsunami transmission theory when evaluating the tsunami transmission attenuation rate, calculate the maximum rise of tsunami design h_(T) required at the actual making point of the tsunami according to the design height of beaching destination h_(g), and take it as the tsunami design value. The evaluation of the design height of beaching destination h_(g) from the tsunami to the beaching destination should be based on the actual topography, as measured by an artificial satellite or aerial photograph, in order to calculate the design height of beaching destination h_(g) where the tsunami can effectively overflow the beaching destination. If a digital topographic map is established through an artificial satellite photograph or an aerial photograph to assist in designing the artificial tsunami, the calculated sea water capacity V_(r) required to meet the height for overflowing can be compared to the calculated data obtained from calculating the projected area. In considering the maximum rise of tsunami design h_(T) in the artificial tsunami design, the factor of safety of the original calculated value is derived, which is about (F.S.)_(T)=1.15˜1.25. List of Symbols AU Potential energy difference U). AK Kinetic energy difference U). i The serial of bombs; no unit. n The quantity of bombs; no unit. $\sum\limits_{i = 1}^{n}{m_{i}h_{i}}$ The quality of Tsunami portion and the product of distance from sea level plus total calculation (m³). TNT Explosion equivalent of the bombs, calculated based on their quality (kg). K(TNT) The brisance of the bombs is the energy emitted after conversion (1 kg TNT=4.184×10⁶ J). K_(e)(TNT) The brisance of a single bomb after being modified by the explosive kinetic energy coefficient is the energy emitted after conversion (1 kg TNT=4.184×10⁶ J). (K_(e)(TNT))_(n) The brisance of a bomb group after being modified by the explosive kinetic energy coefficient is the energy emitted after conversion (1 kg TNT=4.184×10⁶ J). C_(T) The value of the constant of the artificial tsunami is
 79156. D The distance between the coordinate points of the air-dropped bombs and the beaching destination (m). d Underwater penetration of the bombs (m). ρ Standard sea water density of bombs dropped into the ocean is 1025 kg/m³. (F.S.)_(T) The factor of safety of the artificial tsunami; no unit. g(ψ) The standard acceleration of surface gravity is 9.80665 m/s², the precise expression with the earth latitude ψ WGS84 and ellipsoid acceleration of gravity is: ${g(\psi)} = {9.7803253359\frac{1 + {0.00193185265241\mspace{14mu} \sin^{2}\psi}}{\sqrt{1 - {0.00669437999014\mspace{14mu} \sin^{2}\psi}}}}$ ω(d) The explosion waveform coefficient is the function of the underwater penetration of the bombs, the unit of which is m. h_(T) The maximum rise of tsunami design (m). h_(g) The design height of the beaching destination (m). X The maximum rise of tsunami design h_(T) divides the value f(0) of the probability density function; that is, X=h_(T)/f (0); no unit. α The angle (rad) formed by the maximum breadth between the coordinate points of the air-dropped bombs and the beaching destination. β_(T)(ω(d),D) The sea water transmission attenuation rate; no unit. φ(d) The explosive kinetic energy reduction coefficient is the function of the underwater penetration of the bombs; no unit. φ_(e)(S,R_(b)) The modified coefficient of explosive kinetic energy; no unit. φ_(v)(S,R_(ω)) The modified coefficient of sea water capacity; no unit. R_(b) The effective explosion radius (m). R_(ω) The effective radius of the explosion waveform (m). S The bomb group distance (m). V The sea water capacity of the artificial tsunami (m³). V_(r) The sea water capacity for overflowing the beaching destination (m³). V_(e,e) The sea water capacity of a single bomb after being modified by the modified coefficient of explosive kinetic energy (m³). (V_(e,e))_(n) The bomb group sea water capacity after being modified by the modified coefficient of explosive kinetic energy (m³). V_(b,e)(S,R_(b)) The total overlapping of the effective radius of all bombs (m³). V_(b,0)(R_(b)) The total non-overlapping of the effective radius of all bombs (m³). V_(ω,e)(S,R_(ω)) The total overlapping of the effective radius of all bombs according to their explosion waveforms (m³). V_(ω,0)(R_(ω)) The total non-overlapping of the effective radius of all bombs according to their explosion waveforms (m³).
 2. The mentioned pressure gauge and timer are installed on the bombs and dropped into the sea by the bombers to detect water pressure and calculate the time to the water, so as to deduce the underwater penetration. Upon reaching the pressure design value or designated time of the timer, the bombs will explode via one of the systems or after double confirmation. Because the artificial tsunami is a tactic carried out according to precise calculations, and because the underwater penetration control for exploding the bombs is extremely crucial for an artificial tsunami, it is wise to adopt a double confirmation system to explode bombs only after correctly confirming the underwater penetration.
 3. The mentioned bombers and artificial satellite positioning should be precisely positioned, or be based on the coordinate points of the air-dropped bombs as measured by an engineering survey. The bombers can fly at low altitude so as to correctly airdrop the bombs into the sea. If the intention is to avoid enemy radar detection, stealth bombers can be adopted. The bombers should continuously airdrop bombs at the designated coordinate points to create the artificial tsunami, a veritable wall of water, in order to conduct a large-scale beaching operation effectively.
 4. After the said artificial tsunami is calculated correctly, it should be developed on a chart that can be easily referred to or input into computer software to enable military forces to quickly scan the information when in battle. In a real war, soldiers at the frontlines are more likely to know the actual war situation than the logistic units; therefore, the use of an artificial tsunami could be proposed by the frontline soldiers, with the logistic units cooperating with them by dispatching fighters to airdrop bombs and create an artificial tsunami that conforms to the needs of the frontline soldiers. A war environment, due to the complexities of the battlefield, is often not compatible with the use of computer software; therefore, the plan for the artificial tsunami should be drawn into a chart that can be conveniently carried. In chart form the plan will have a 5% scanning difference as the result of being printed out, which should be taken into account, and the explosion energy K(TNT) should be reduced to 95%. The chart should be printed with A2 or above graph paper in order to avoid a failure to meet the design standard in the war.
 5. The said artificial tsunami is used together with a military force, so a new type of soldier the tsunami soldier, is required. The training mode of tsunami soldiers is similar to the assessment of a mathematical operation. It is necessary that they quickly calculate the height for the overflowing of the beaching destination, i.e. the design height of beaching destination h_(g), and sea water capacity V_(r) according to different topography, as well as calculate the maximum rise of tsunami design h_(T) and sea water capacity V_(e,e) of the air-dropped bombs according to distance D and tsunami transmission attenuation rate β_(T)(ω(d),D) and determine the explosion equivalent TNT and underwater penetration d after scanning the chart of the artificial tsunami. The artificial tsunami design is the same for a single bomb artificial tsunami as it is for a bomb group, but the bomb group effect and the designed bomb group distance S should be taken into account. The standard for designing an artificial tsunami should take the maximum rise of tsunami design h_(T) as the priority, and then decide sea water capacity V_(e,e) or (V_(e,e))_(n) on the basis of the artificial tsunami. However, it must be kept in mind that, due to numerous causes (such as the drain of sea water), not all of the sea water capacity can be used for the beaching destination. Explosion equivalent TNT and underwater penetration d must be determined and, under the circumstance of tsunami transmission attenuation rate β_(T)(ω(d),D), it checked whether or not the design demand of overflowing the beaching destination can be met. In considering the bomb group effect, the modified coefficient of the explosive kinetic energy φ_(e)(S,R_(b)) and modified coefficient of sea water capacity φ_(v)(S,R_(ω)) should be used to modify the brisance and sea water capacity. Whether tsunami soldiers can pass the assessment depends on whether the results of the artificial tsunami are above the design requirements; nevertheless, over-design should be avoided so as to reduce war expenditures. The number of tsunami soldiers required is small, so they should be carefully selected and distributed to the marine forces.
 6. With the said artificial tsunami, it is recommended to airdrop bombs between two o'clock and five o'clock in the morning, and to dispatch military forces to take over the beaching destination after the ebb of the tsunami at six or seven in the morning in order to reduce the number of casualties from the military forces. After the artificial tsunami has swept over the enemy forces, the interval during which the military forces take control must be tight enough to minimize the possibility of the attacking forces being ambushed by the enemy. Thus, the time by which the military forces must take over after the artificial tsunami should be arranged and planned efficiently. When taking over the beaching destination, the military forces should dispatch the air force to shield the ground forces so they will not be subject to an enemy attack.
 7. The said artificial tsunami could also be used for civilian purposes, such as to lower the cost of fishing at sea by fishermen. Fishermen could jointly purchase bombs to be dropped into the sea to create an artificial tsunami which would bring schools of fish nearer the port and enable their easy capture. 